1. ARA0103 Aðferðafræði Rannsókna
Fyrirlestur 15 Factorial designs/Þáttasnið
factor/þáttur
21/09/2018
Dr Andy Brooks

2. Factorial Designs/Þáttasnið
True experimental design/Hrein tilraun
Factorial Designs/Þáttasnið
True experiments can consider more than one independent variable.
We could consider the effects of mattress cover and the frequency of patient turning on the number of bedsores.
tvær óháðar breytur
We could consider the effects of mattress cover, the frequency of patient turning, and nutritional supplements on the number of bedsores.
þrjár óháðar breytur
háð breyta : fjöldi legusára
21/09/2018
Dr Andy Brooks

3. 4 hópar -> margir sjúklingar
Dæmi: þáttasnið, 2x2 snið
mattress cover
Usual mattress M1
Sheepskin M2
Usual frequency of patient turning F1
M1 F1
M2 F1
x2 frequency of patient turning F2
M1 F2
M2 F2
að snúa
sjúklingum
The two factors are: mattress cover and frequency of patient turning.
Factors must have two or more levels.
This is a 2x2 design.
4 hópar -> margir sjúklingar
21/09/2018
Dr Andy Brooks

4. Multiple hypotheses/Margar tilgátur
Factorial designs allow the testing of many hypotheses in a single experiment.
Do sheepskin covered mattresses reduce bedsores? (main effect/megináhrif)
Does doubling the frequency of patient turning reduce bedsores? (main effect/megináhrif)
Are sheepskin mattresses more effective at a particular frequency of patient turning? (interaction effect/samvirkniáhrif)
21/09/2018
Dr Andy Brooks

5. One-way ANOVA test Eins þáttar ANOVA próf
Not a factorial design.
One-way ANOVA test Eins þáttar ANOVA próf
analysis of variance
fervikagreining
t-próf, tveir hópar
eins þáttur ANOVA próf, þrír eða fleiri hópar
dæmi:
There are 3 groups of 10 patients.
The patients have memory problems.
Ég man ekki...
Each group is given a different intervention (inngrip A, B, or C) which should help them remember things.
After the intervention, the patients are given a memory test/minnispróf and their scores recorded.
The null hypothesis is that the means for the three groups are the same.
Núlltilgátan – meðaltöl eru jöfn/áhrif er ekki til
21/09/2018
Dr Andy Brooks

6. Árangur minnisprófa A B C 3 10 20 5 8 15 14 2 9 4 11 17 6 16 7 18 19
21/09/2018
Dr Andy Brooks

7. One-way ANOVA results Við getum hafnað núlltilgátunni (p < 0,01).
Anova: Single Factor
SUMMARY
Groups
Count
Sum
Average
Variance
Column 1 10 53
5,3
8,011111
Column 2
118
11,8
13,06667
Column 3
147
14,7
16,01111
ANOVA
Source of Variation SS df MS F
P-value
F crit
Between Groups
463,4 2
231,7
18,74146
7,87E-06
3,354131
Within Groups
333,8 27
12,36296
Total
797,2 29 0,
Við getum hafnað núlltilgátunni (p < 0,01).
21/09/2018
Dr Andy Brooks
Hin tilgátan er rétt.

8. Eins þáttar ANOVA árangur
Hin tilgátan er rétt, en samt, við vitum ekki:
Er A betri en B?
Er B betri en C?
Er A betri en C?
Special follow-up tests can be performed.
Do not perform several t-tests as this effects the alpha levels (0,05 and 0,01).
Special follow-up tests are an advanced topic.
So plot a graph/Svo teikna graf
You may get the answer you seek by looking at boxplots.
21/09/2018
Dr Andy Brooks

9. Boxplot/Kassarit Inngrip B og C eru betri en A.
50% of the data lies in the box.
lágmark
miðtala
hámark
Inngrip B og C eru betri en A.
En B og C skarast mikið.
21/09/2018
Dr Andy Brooks

10. Two-way ANOVA test tveggja þátta ANOVA próf
hayfever/heymæði
Two-way ANOVA test tveggja þátta ANOVA próf
skor í bílprófshermi
A new drug is a good remedy for hay fever, but it may effect performance when driving a car. It is possible that the effects on people who have been drinking alcohol are different to those who have not been drinking alcohol.
Factor 1: placebo, usual drug, new drug
gervilyf, venulegt lyf, nýtt lyf
Factor 2: no alcohol, alcohol
án áfengis, áfengi
Háð breyta: skor í bílprófshermi.
Hver flokkur með 10 þátttakendum.
3 x 2 snið
Factorial Design/Þáttasnið
21/09/2018
Dr Andy Brooks

11. Experimental Data (Excel format) placebo usual drug new drug
No alcohol 24 18 27 25 8 14 13 9 19 22 29 16 23 15 6 17 20 26
Alcohol 21 12 11 4 3 2
Experimental
Data
(Excel format)
21/09/2018

12. Two-way ANOVA results The null hypotheses are rejected (p < 0,01).
Source of Variation SS df MS F
P-value
F crit
Sample
201,6667 1
8,712
0,004669
4,019541
Columns
190 2 95
4,104
0,021917
3,168246
Interaction
763,3333
381,6667
16,488
2,58E-06
Within
1250 54
23,14815
Total
2405 59
Sample is Factor 2
Columns is Factor 1
The null hypotheses are rejected (p < 0,01).
Núlltilgáturnar eru hafnað (p < 0,01).
21/09/2018
Dr Andy Brooks

13. Anova: Two-Factor With Replication
SUMMARY
placebo
usual drug
new drug
Total
No alcohol
Count 10 30
Sum
210
120
220
550
Average 21 12 22
18,33333
Variance
18,44444
19,55556
24,44444
40,29885
Alcohol
100
180
160
440 18 16
14,66667 32
21,55556
22,88889
35,67816 20
310
300
380
15,5 15 19
55,73684
28,94737
31,89474
21/09/2018

14. Line graph showing averages Línurit sýna meðaltöl
teikna graf
Line graph showing averages Línurit sýna meðaltöl
no alcohol
alcohol
21/09/2018
Dr Andy Brooks

15. Preliminary conclusions from the experiment
preliminary conclusions/drög að niðurstöðum
Preliminary conclusions from the experiment
The usual drug has a bad effect on driving performance for drivers who have not been drinking alcohol.
Both the usual and new drugs have a good effect on driving performance for drivers who have been drinking alcohol.
Overall the new drug outperforms the usual drug.
Assuming it is as good a remedy for hay fever as the old drug.
21/09/2018
Dr Andy Brooks

16. Caution/Viðvörun
It can be very complicated analysing factorial designs bigger than 3x3.
...gæti verið afar flókið að greina þáttasnið stærri en 3x3
From a statistical point of view, follow-up tests are required if you have significant main and interaction effects.
Plotting the data as boxplots or line charts of averages can allow preliminary conclusions to be made.
21/09/2018
Dr Andy Brooks